Optimum distribution of additional reinforcement to reduce differential column shortening

Abstract

Summary Differential column shortening should be reduced to mitigate the adverse effects caused by such shortening in a tall building. The axial stiffness of columns with greater shortening than adjacent columns should be increased to reduce the differential column shortening. The axial stiffness of the columns can be effectively increased by utilizing additional reinforcement for them. The optimum distributions of this additional reinforcement to reduce the differential column shortening in a tall building are determined. An optimization problem is formulated to minimize the total amount of reinforcement. Three analysis models, namely a fixed-section, fixed-stress and general model, are presented as numerical examples. The contour plots for a two-variable problem of the three analysis models are presented. The generalized reduced gradient method is applied to obtain the optimum solutions of multi-variable problems. The differential column shortenings after optimization confirm that the optimization program developed in this study can yield the optimum distributions of additional reinforcement.